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A transience condition for a class of one-dimensional symmetric Lévy processes


 
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1. Title Title of document A transience condition for a class of one-dimensional symmetric Lévy processes
 
2. Creator Author's name, affiliation, country Nikola Sandrić; University of Zagreb; Croatia
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) characteristics of a semimartingale; electrical network; L\'evy measure; L\'evy process; random walk; recurrence; transience
 
3. Subject Subject classification 60G17; 60G50; 60G51
 
4. Description Abstract

In this paper, we give a sufficient condition for the transience for a class of one dimensional symmetric Lévy processes. More precisely, we prove that  a one dimensional symmetric Lévy process with the Lévy measure $\nu(dy)=f(y)dy$ or $\nu(\{n\})=p_n$, where the density function $f(y)$ is such that $f(y)>0$  a.e. and the sequence $\{p_n\}_{n\geq1}$ is such that $p_n>0$ for all $n\geq1$, is transient if $$\int_1^{\infty}\frac{dy}{y^{3}f(y)}<\infty\quad\mbox{or}\quad\sum_{n=1}^{\infty}\frac{1}{n^{3}p_n}<\infty.$$  Similarly, we derive an an alogous transience condition for one-dimensional symmetric random walks with continuous and discrete jumps.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2013-08-24
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2802
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2802
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
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